Network Utility Maximization with Nonconcave, Coupled, and Reliability-based Utilities

Network Utility Maximization (NUM) has significantly extended the classical network flow problem and provided an emerging framework to design resource allocation algorithms such as TCP congestion control and to understand layering as optimization decomposition. We present a summary of very recent results in the theory and applications of NUM. We show new distributed algorithms that converge to the globally optimal rate allocation for NUM problems with nonconcave utility functions representing inelastic flows, with coupled utility functions representing interference effects or hybrid social-selfish utilities, and with rate-reliability tradeoff through adaptive channel coding in the physical layer. We conclude by discussing how do different decompositions of a generalized NUM problem correspond to different layering architectures.